Some novel versions of fractional hermite–hadamard-mercer type inequalities with matrix applications

In this study, we explore several fractional Hermite–Hadamard (H–H)-Mercer inequalities for inter-val-valued functions through the use of a generalized fractional integral operator (GFIO). Further-more, we examine new variations of the H–H-Mercer inequality in relation to GFIO. Various examples are included to support our assertions. The results could offer new insights into a broad spectrum of integral inequalities for fractional fuzzy systems within the framework of interval analysis, along with the optimization issues they raise. Moreover, some applications on matrices are illustrated.